My inquiry is to what is causing my car's engine to not turn over. Here are the facts:

-Whan you turn the key, the engine does not even attempt to turn over and makes no noise at all.
-The radio and air conditioning works and so do warning sounds (like when the door is left ajar).
-The battery is fully charged according to the meter reading I got, but there is a lot of corrosion on the positive end of it.
-The three suggestions I have gotten so far are battery problems (dead cell/bad connection), a broken fuse, or starter problems.

What do you guys think?
I'm not sure what to look for to see if it is a blown fuse. I also am not sure how to check for sure that it is either of the other options.

Quick check on the battery and starter... Grab a multimeter, set it to 20 volts, lay across the battery terminals and have someone try to start the car... Does the voltage drop? If so, how much. On the lowest resistor setting, check the wiring between the positive on the battery to the starter. Clean your battery terminals as well.

Sure hope it's not a timing belt, but it's also a good place to start. you can try to manually crank the engine over gently with a socket on the crank. If it cycles cleanly then it's probably not the belt.

if it was the timing belt it would still crank but not start. check the relays and fuses

As many others also point out, it wont turn over if the cam belt is gone and the pistons are obstructed by the open (or broken) valves.

To the OP, if it's a manual gearbox try a push start, and if the engine doesn't turn over then, you can rest assured that the cam belt is gone.
If it does turn over, then you need to check the connections on main power cable to the starter and all the grounds, and of course the fuses.

If it is a broken cam belt, you should still hear the starter motor respond, and the dash lights would dim.

When mine went, the engine wouldn't turn over at all. I was there when they tore the engine down (few other engines lying around too, same problem). Holes in 3 pistons, yes, but it was jammed up. So saying that everytime they break isn't a fair assumption.